The purpose of this thesis was to explore computationally the three dimensional hydrodynamics of extragalactic radio jets. This entailed putting together a large number of numerical tools before such simulations could be performed. The thesis was structured to be a set of papers, each addressing a computational or astrophysical issue that was important in completing the objective of this thesis. Three chapters on numerical techniques are presented testing out both particle and grid-based methods for computational fluid dynamics. Then follow four chapters of astrophysical applications. The first of those considers the flow of a supersonic jet in a transonic cross-wind as a model for narrow angle tails. The second considers jet-shock interactions as a model for wide angle tails. The third tries out jet-cloud interactions as a model for the largest of wide angle tails. The fourth uses wall-jets as a model for hot spot formation.